You are right that one can track more closely how wave function collapse occurs, say by looking at how random noise from the macroscopic instrument creeps into the calculation and causes decoherence. But my point is that criticizing the Copenhagen interpretion on the grounds that it does not track that process is like criticizing the ideal gas law because it doesn't tell us where every particle goes. All physical theories decide what they are going to care about, and what they will sweep under the rug, and the idea that any physical theory can be "complete" is just not recognizing what physics does. Some theories are more fundamental than others, but that's all one can ever say. The idea that any are "really fundamental" is a claim that I always find pretty puzzling, even though good physicists seem to claim things like that. They seem to have simply forgotten what they chose to pretend.